This invention relates to a system for producing a digital representation of the value of an angle .theta. from two first analogue quantities respectively representative of A sin .theta. and A cos .theta., where A is an amplitude factor, comprising
first means for deriving from the two first analogue quantities a plurality of n second analogue quantities which are functions of .theta. such that in each of n contiguous portions of a total angular range for .theta. of 2.pi. radians, each portion extending over 2.pi./n radians, the value of a respective third analogue quantity which is derivable from two of the second quantities and which is independent of A lies within a predetermined range of values,
second means, comprising comparison means, for deriving from the second analogue quantities a first digital quantity representative of which one of the n portions the value of .theta. lies in,
third means, comprising selection means controlled by said first digital quantity and analogue-to-digital conversion means, for deriving a second digital quantity representative of the value of the respective third analogue quantity whose value lies within said predetermined range of values and thereby being representative of the value of .theta. within said one portion, and
fourth means for deriving from the first and second digital quantities a digital representation of .theta.. The angle .theta. may for example be a phase angle.
U.S. Pat. No. 4,390,865 discloses such a system, being an apparatus for digital position measurements, for example for machine tools. In this apparatus, there are derived from quantities representing sin .alpha. and cos .alpha. four quantities respectively representing sin .alpha., sin .alpha., cos .alpha. and cos .alpha.. Logic circuitry including comparators derives from these quantities a digital representation of which of eight octants of an angular range of 2.pi. radians the value of the angle .alpha. lies in. This digital representation controls selectors which select two of the four quantities; a digital representation of the quotient of the two selected quantities is produced by an analogue to digital converter, the denominator of the quotient serving as a reference voltage in the converter. The two quantities are selected to satisfy the requirement that the value of their quotient lies between zero and (1/.sqroot.2). The digital representation of the quotient is supplied to a ROM coupled to a micro-processor which also together receive the digital representation of the octant and therefrom derive a digital representation of .alpha..
Such an apparatus has the disadvantage of being unsuited for applications in which the amplitude factor A in the quantities representing the sin .alpha. and cos .alpha. may vary over a substantial range, since analogue-to-digital converters require a reference voltage (which in this instance is the denominator of the quotient) to lie within a small range to ensure satisfactory operation; the converters are furthermore not capable of very high speed operation when used to form a quotient in this manner, and the use of a microprocessor also restricts the speed of operation.